Heavy-quark Potential by AdS/CFT and Color SuperCond. in Dense QCD

侯德富　

华中师范大学粒子物理研究所

十三届中高能核物理大会，合肥

• Motivations • Holographic study of heavy quarkonium • Color Superconductivity in dense QCD• Summary

OUTLINES

pair dissociation line

Tc

(1.5-2) Tc

Color SuperConductor.

sQGP (Shuryak)

Motivations

Heavy quarkonium from AdS/CFT

Heavy quark potential probes the confinement in hadronic matter and meson melting in plasma

AdS/CFT at finite temperature

Classical Supergravity on AdS-BH×S5

4dim. Large-Nc strongly coupledSU(Nc) N=4 SYM at finite temperature(in the deconfinement phase).

conjecture

=

Witten ‘98 Maldacena ‘97

Potential from AdS/CFT

bounded by the loop C, when y goes to infinity, y->1 BH

Wilson-loop at finite temperature

Minimizing the world sheet area (the Nambu-Goto action)

qq r qq r

BH

y

F(r,T)

r

r0

Dissociate Temperature Hou, Ren JHEP01 (08)

),(

2expexp][

XSi

ddXAdxiCWC

Strong couping expansion

Semi-classical expansion

...

][0 ,][ln

Cb

XSiCW

X = the solution of the classical equation of motion;

b[C] comes from the fluctuation of the string world sheet around X

,

more significant than 3 -correction for Wilson loops.

Gravity dual of a Wilson loop

Parallel lines ：

Straight line ：4

31 3 5

2 22 2

det ( )[ ] ln

det ( 2)det ( )

iW C

43

2 1 52 2 22 2

det ( )[ ] ln

det( 2)det ( 4 )det ( )

iW C

R

Wilson-loop at sub-leading order

)()det2det(-24det

4

11det

4

11-det

22

52)2(22

1

)2(22)2(22

R

RRZ

Partition function at finite T with fluct.

Straight line ：

Parallel lines ：

Hou, Liu, Ren, PRD80,2009

Chu, Hou, Ren,JHEP0908,(09)

2

4

4 1.33460 1( ) [1 ( )]

1( )4

V r Or

Subleading order Results

Erickson etc. NPB582, 2000

Subleading order potential @ Finite T

Ground state of dense quark matter

(i) Deconfined quarks( )(ii) Pauli principle(s=1/2)

(i) Effective models( )(ii) One-gluon exchange( )

Cooper instability

Color superconductivity

5( ) 0Ci j

QCD

QCD QCD

Color SuperConductivity

B. Barrois, NPB 129, 390 (1977)D. Bailin and A. Love, Phys. Rep. 107,325 (1984)M. Alford et al., PLB 422, 247 (1998)R. Rapp et al., PRL 81, 53 (1998)

• No reliable lattice results at finite density • effective models of dense QCD

• Additional complications due to

charge neutrality and \beta equilibrium

• Difficulties in determining stable ground states

QCD at large baryon density

1 1 1 12

1[ , ] { ln ( 1) ln ( ) 2 [ , ]

2D S Tr D Tr D D Tr S Tr S S D S

Powers of TStationary points

Order of g^2mu^4

CJT action of dense QCD

D. Rischke Prog. Part. Nucl. Phys. 52 197 (2004)

1 1 10

1[ , ] [ ln ln ( 1)]

2

n

D S Tr D Tr S Tr S S

F

Energy density of normal phase Free energy density

0F Gap equationMinimization of F

Ginnakis, Hou, Ren, Rischke, PRL 93 (04) ; PRD73 (06)

Gauge field fluc. induce 1st order PT

CSC at moderate density:

• Beta equilibrium• Non-zero strange quark mass• Charge neutrality

Fermi momentummismatch

Single flavor CSC

M. Alford et al., Rev. Mod. Phys. 80, 1455 (2008)

• Spherical states

• Non-spherical states

0ˆ ˆ(0, ) ( )M Mp f p

Most stable state

Angular momentum mixing(I)

A. Schmitt, PRD 71, 054016 (2005)

• Helium_3

• QCD

11( ) (cos ) (2 1) (cos ) 3l

l ll

V k k V l V P V k k

Pairing potential:

Nonlinear gap equation:

Angular momentum mixing

0 0 1ˆ ˆ(0, ) ( ) (cos )p f p P

Angular momentum mixing(II)

Angular momentum mixing lowered the free energy of the non-spherical stateTransv. CSL is the most stable phase even with AMM mixing

Ground states of single flavor CSC

ASchmitt, PRD 71, 054016 (2005) Feng, Hou , Ren, NPB 796, 500 (2008); NPB 813, 408 (2009); J Phys. G 36, 045005 (2009)

• Typical magnetic field ～ 10^12G• Meissner effects in spin 1 CSC

Single flavor in magnetic field

Schmitt , wang, Rischke., PRL 91, (2003)

Feng, Hou, Ren, Wu, in pareparation

• AdS/CFT is a useful tool to study strongly coupled gauge field theory

• Viscosity, /s. Thermodynamics. Jet quenching• Photon production, Friction ,Heavy quarkonium • Hardron spectrum (ADS/QCD)

• Angular momentum mixing in non-spherical states is important

• Non-spherical states could be the ground state in neutron starts

Summary